Constrained regional control problem of a bilinear plate equation

ABSTRACT

This paper investigates a regional optimal control problem of a plate equation described by a bilinear system evolving in a spacial domain Ω. The control is distributed, bounded and acts on the velocity term. Then, we minimise a functional cost constituted of the deviation between a desired state and the reached one only on a subregion ω of Ω and the energy term. The purpose of this study is to prove that a control solution of such problem exists, and characterised as a solution to an optimality system. Numerical approach is given and successfully illustrated by simulations.

Keywords:

• Distributed bilinear systems
• plate equation
• controllability
• optimal control

Acknowledgments

The authors would like to thank the anonymous referees for their valuable comments.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work was supported by Hassan II Academy of Sciences and Technology (Académie Hassan II des Sciences et Techniques) [630/2016].